Euler's constants for the Selberg and the Dedekind zeta functions

Yasufumi Hashimoto, Yasuyuki Iijima, Nobushige Kurokawa, Masato Wakayama

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11 Citations (Scopus)

Abstract

The purpose of this paper is to study an analogue of Euler's constant for the Selberg zeta functions of a compact Riemann surface and the Dedekind zeta function of an algebraic number field. Especially, we establish similar expressions of such Euler's constants as de la Vallée-Poussin obtained in 1896 for the Riemann zeta function. We also discuss, so to speak, higher Euler's constants and establish certain formulas concerning the power sums of essential zeroes of these zeta functions similar to Riemann's explicit formula.

Original languageEnglish
Pages (from-to)493-516
Number of pages24
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Volume11
Issue number4
Publication statusPublished - Oct 1 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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  • Cite this

    Hashimoto, Y., Iijima, Y., Kurokawa, N., & Wakayama, M. (2004). Euler's constants for the Selberg and the Dedekind zeta functions. Bulletin of the Belgian Mathematical Society - Simon Stevin, 11(4), 493-516.